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Block RAMs (BRAMs) are the storage houses of FPGAs, providing extensive on-chip memory bandwidth to the compute units implemented using Logic Blocks (LBs) and Digital Signal Processing (DSP) slices. We propose modifying BRAMs to convert them to CoMeFa (Compute-In-Memory Blocks for FPGAs) RAMs. These RAMs provide highly-parallel compute-in-memory by combining computation and storage capabilities in one block. CoMeFa RAMs utilize the true dual port nature of FPGA BRAMs and contain multiple programmable single-bit bit-serial processing elements. CoMeFa RAMs can be used to compute in any precision, which is extremely important for evolving applications like Deep Learning. Adding CoMeFa RAMs to FPGAs significantly increases their compute density. We explore and propose two architectures of these RAMs: CoMeFa-D (optimized for delay) and CoMeFa-A (optimized for area). Compared to existing proposals, CoMeFa RAMs do not require changing the underlying SRAM technology like simultaneously activating multiple rows on the same port, and are practical to implement. CoMeFa RAMs are versatile blocks that find applications in numerous diverse parallel applications like Deep Learning, signal processing, databases, etc. By augmenting an Intel Arria-10-like FPGA with CoMeFa-D (CoMeFa-A) RAMs at the cost of 3.8% (1.2%) area, and with algorithmic improvements and efficient mapping, we observe a geomean speedup of 2.5x (1.8x), across several representative benchmarks. Replacing all or some BRAMs with CoMeFa RAMs in FPGAs can make them better accelerators of modern compute-intensive workloads.